Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines
This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions, and then we show that the re...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/593436 |
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| _version_ | 1849414366824235008 |
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| author | Yeon Ju Lee Jungho Yoon |
| author_facet | Yeon Ju Lee Jungho Yoon |
| author_sort | Yeon Ju Lee |
| collection | DOAJ |
| description | This paper is concerned with analyzing the mathematical properties, such as the
regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines.
We first discuss the biorthogonality condition of the nonstationary refinable functions,
and then we show that the refinable functions based on exponential B-splines have the same
regularities as the ones based on the polynomial B-splines of the corresponding orders. In the
context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of
a refinable function. For this reason, we prove that the suggested nonstationary wavelets form
Riesz bases for the space that they generate. |
| format | Article |
| id | doaj-art-6d456a2823ec4c7ba2fea9206df05a5d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6d456a2823ec4c7ba2fea9206df05a5d2025-08-20T03:33:51ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/593436593436Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-SplinesYeon Ju Lee0Jungho Yoon1Department of Mathematical Sciences, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of KoreaDepartment of Mathematics, Ewha Womans University, Seoul 120-750, Republic of KoreaThis paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions, and then we show that the refinable functions based on exponential B-splines have the same regularities as the ones based on the polynomial B-splines of the corresponding orders. In the context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of a refinable function. For this reason, we prove that the suggested nonstationary wavelets form Riesz bases for the space that they generate.http://dx.doi.org/10.1155/2011/593436 |
| spellingShingle | Yeon Ju Lee Jungho Yoon Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines Abstract and Applied Analysis |
| title | Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines |
| title_full | Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines |
| title_fullStr | Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines |
| title_full_unstemmed | Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines |
| title_short | Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines |
| title_sort | analysis of compactly supported nonstationary biorthogonal wavelet systems based on exponential b splines |
| url | http://dx.doi.org/10.1155/2011/593436 |
| work_keys_str_mv | AT yeonjulee analysisofcompactlysupportednonstationarybiorthogonalwaveletsystemsbasedonexponentialbsplines AT junghoyoon analysisofcompactlysupportednonstationarybiorthogonalwaveletsystemsbasedonexponentialbsplines |